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Related theorems GIF version |
| Description: Define the range of a class. For an alternate definitions, see dfrn2 3394, dfrn3 3395, and dfrn4 3590. |
| Ref | Expression |
|---|---|
| df-rn | ⊢ ran A = dom ◡ A |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cA | . . 3 class A | |
| 2 | 1 | crn 3252 | . 2 class ran A |
| 3 | 1 | ccnv 3250 | . . 3 class ◡A |
| 4 | 3 | cdm 3251 | . 2 class dom ◡ A |
| 5 | 2, 4 | wceq 992 | 1 wff ran A = dom ◡ A |
| Colors of variables: wff set class |
| This definition is referenced by: dfrn2 3394 dmcnvcnv 3423 rncnvcnv 3424 rneq 3426 rnss 3429 brelrng 3430 rncoss 3451 rncoeq 3454 rnun 3542 rnin 3543 rnxp 3557 rnsnop 3582 op2nda 3584 dfco2a 3599 unidmrn 3621 cnvexg 3624 fncnv 3666 funcnvres 3673 funimacnv 3676 fimacnvdisj 3756 dff1o4 3804 f1ocnv 3809 foimacnv 3814 tz7.48-3 4259 sbthlem5 4596 sbthlem8 4599 sbthlem9 4600 fodomr 4628 inf3lem7 4764 zorn2lem4 4937 fodom 4944 uzrdgvali 6666 cnconst 7990 adj1o 10098 ranncnt 10873 toplat 10884 cvimarndm 11406 ordtypelem4 11430 opncldf1 11454 compfipin0lem 11492 compfipin0 11493 cnvcan 11814 f1ocan1fv 11816 |